Question

If a hospital receives an average of 6 patients who are on critical condition, what is the probability that it will receive

i). 4 patients on a critical condition on any given day?

ii). 10 Patients on a critical conditions over any 2 consecutive days

Answer 1

i) Let X denotes the number of patients on a critical condition on any given day.

X ~ Poisson(6)

The probability mass function of X is

The probability that it will receive 4 patients on a critical condition on any given day

ii) Let Y denotes the number of patients on a critical condition over any 2 consecutive days.

Y ~ Poisson(6*2) or Y ~ Poisson(12)

The probability mass function of Y is

The probability that it will receive 10 patients on a critical condition over any 2 consecutive days